Geology Reference
In-Depth Information
Fig. 8.4
P
wave and
S
wave velocity as a function
of depth. Values are plotted
from the PREM seismic
model of the Earth
(Dziewonski and Anderson
1981
).
CMB
is the
core-mantle boundary,
ICB
is the inner core boundary
0
2000
4000
6000
8000
10000
12000
[kg m
-3
]
14000
r
0
1000
2000
CMB
3000
4000
ICB
5000
6000
Depth
[km]
7000
Fig. 8.5
Rock density as a function of depth. Values are plotted from the PREM seismic model of the Earth
(Dziewonski and Anderson
1981
).
CMB
is the core-mantle boundary,
ICB
is the inner core boundary
An important class of solutions to the plane
waves Eq. (
8.12
) is represented by periodic func-
tions having the form:
the spatial distribution of the monochromatic
wave:
¨
2
'
2
0
D
0
2
0
C
r
(8.31)
.r;t/
D
0
.r/ cos.¨t
C
ª/
(8.30)
This is a scalar Helmholtz's equation, similar
to that encountered in Sect. 4.8. We know that
the solutions to this equation are combinations of
sines and cosines:
where ª is the
phase
, ¨ is the angular frequency,
and
D
¨/2 is the wave frequency. Solutions
of the form (
8.30
) are called
monochromatic
waves
.
Substituting
(
8.30
)into
8.12
)gives
0
.r/
D
e
i kr
(8.32)
a
time-independent
equation
that
determines